Jean-Luc Fouquet

On graphs without P 5 and P¯ 5

Abstract We extend results due to Blazsik et al. (1993) on graphs with no induced C 4 and 2 K 2 to the self-complementary class of ( P 5 , P 5 )- free graphs. Moreover, we obtain an O(ω 2 ) γ -binding function for this last class of graphs, answering thus partially a question of A. Gyarfas.

On ( K q , k ) vertex stable graphs with minimum size

Abstract A graph G is a ( K q , k ) vertex stable graph if it contains a K q after deleting any subset of k vertices. We give a characterization of ( K q , k ) vertex stable graphs with minimum size for q = 3 , 4 , 5 .

On Parsimonious Edge-Colouring of Graphs with Maximum Degree Three

In a graph G of maximum degree Δ, let γ denote the largest fraction of edges that can be Δ edge-coloured. Albertson and Haas showed that

Domination, coloring and stability in P 5 -reducible graphs

{gamma geq frac{13}{15}}

On Minimum (Kq, K) Stable Graphs

when G is cubic. We show here that this result can be extended to graphs with maximum degree 3, with the exception of a graph on 5 vertices. Moreover, there are exactly two graphs with maximum degree 3 (one being obviously the Petersen graph) for which

On transversals in minimal imperfect graphs

{gamma = frac{13}{15}.}